1. Field of the Invention
This invention relates to a method and apparatus for constructing a two-dimensional picture of an object slice from linear projections of radiation not absorbed by the object, useful in the fields of medical radiology, microscopy, and non-destructive testing. The branch of the invention employing x-rays for medical radiology is sometimes referred to as computerized tomography.
2. Description of the Prior Art
It is useful in many technologies to construct a two-dimensional pictorial representation from a series of linear data resulting from sensory projections taken through a quasi-plane within which lies the two-dimensional planar slice of the object that one wishes to reconstruct. For example, in the case of utilizing X-rays to provide a pictorial representation of the inside of a human body it is known to pass X or gamma radiation through the tissues of the body and measure the absorption of this radiation by the various tissues. The nature of the tissues may then be determined by the percentage extent of absorption in each tissue of the radiation, since different tissues are known to absorb differing amounts of radiation.
Passing a wall of radiation through an object and detecting the amount of absorption within the object by means of complementary-spaced detectors results in a three-dimensional object being projected onto a two-dimensional picture. This can result in the superimposition of information and resulting loss of said information. More sophisticated techniques must be devised if one wishes to examine a body with greater sensitivity to spatial variations in radiation absorption and fewer superimposition effects.
In a method known as general tomography a source of radiation and a photographic film are revolved along an elliptical or other path near the body in such a way that elements in one plane of the body remain substantially stationary. This technique is utilized to obtain relevant information along a two-dimensional planar slice of the body. This method has a disadvantage in that shadows of bodily tissues on planes of the body other than the desired planar slice appear as background information partially obscuring the information desired to be obtained from the cognizant slice.
In an attempt to obtain more accurate information, methods have been proposed whereby the radiation and detection of small all lie within the planar slice of the object to be examined. A two-dimensional reconstruction of the thin slice of the object is then performed, and repeated for each slice desired to be portrayed or diagnosed.
In A. M. Cormack, "Representations of a Function by Line Integrals with Some Radiological Applications", Journal of Applied Physics, Vol. 34, No. 9, pp. 2722-2727, (September 1963), (reference 1), the author used a collimated 7 millimeter diameter beam of cobalt 60 gamma rays and a collimated Geiger counter. About 20,000 counts were integrated for each 5 millimeter lateral displacement of the beam which passed through a phantom 5 centimeters thick and 20 centimeters in diameter comprising concentric cylinders of aluminum, aluminum alloy and wood. Because of symmetry of the phantom, measurements were made at only one angle. The resulting calculated absorption coefficients were accurate to plus or minus 1.5 percent.
In October, 1964, the same author in "Representations of a Function by Line Integrals with Some Radiological Applications. II", Journal of Applied Physics, Vol. 35, No. 10, pp 2908-2913, (2), separated the two-dimensional problem into a set of one-dimensional integral equations of a function with solely radial variation. The measurements were expanded in a sine series with coefficients identical to those of the radial density function when expanded in a limited series of Zernicke polynomials. This method is mathematically equivalent to a Fourier transform technique but differs in practical application, such as significance of artifacts introduced by interpolation. Cormack used a collimated 5.times.5 millimeter beam of cobalt 60 gamma rays and a collimated Geiger counter. About 20,000 counts were integrated for each beam position. The beam was displaced laterally by 5 millimeter intervals to form a parallel set of 19 lines and the set was repeated at 7.5 degree intervals for 25 separate angles. The phantom was 2.5 centimeters thick, 20 centimeters in diameter, comprising an aluminum disc at the center, an aluminum ring at the periphery, an aluminum disc off axis, and the remainder Lucite. From 475 independent measurements, 243 constants were determined and used to synthesize the absorption distribution. The resulting accuracy of calculated absorption values was good on average but ringing was introduced by the sharp changes in density. Cormack's method is capable in theory of yielding a unique principal solution, but is nevertheless complicated, has limited practical application and is liable to error in its practically feasible forms.
D. J. DeRosier and A. Klug in "Reconstruction of Three-Dimensional Structures from Electron Micrographs", Nature, Vol. 217, pp. 130-134 (Jan. 13, 1968), (3), used Fourier transformation of two-dimensional electron transmission images (electron micrographs) at a number of angles (30 for nonsymmetric objects) to produce a series of sections representing the object in three dimensions. Resolution of the final three-dimensional Fourier density map was 30 Angstroms, for a 250 Angstrom T4 bacteriophage tail.
R. G. Hart, "Electron Microscopy of Unstained Biological Material: The Polytropic Montage", Science, Vol. 159, pp. 1464-1467 (March, 1968), (4), used 12 electron micrographs taken at different angles, a flying spot scanner, cathode ray tube and a CDC-3600 computer (Control Data Corporation, Minneapolis, Minn.) with 48 bit, 32K word core to produce a section display by digital superposition. Resolution approached 3 Angstroms.
D. E. Kuhl, J. Hale and W. L. Eaton, "Transmission Scanning: A Useful Adjunct to Conventional Emission Scanning for Accurately Keying Isotope Deposition to Radiographic Anatomy", Radiology, Vol. 87, pp. 278-184, in August, 1966, (5), (see FIG. 10) installed a collimated radioactive source (100 millicuries of 60 keV Americium-241) opposite one detector of a scanner which had two opposed detectors. (Kuhl also suggested that a 1 millicurie 30 keV Iodine-125 source could be installed opposite each of the detectors of a two detector sytem.) A 6.3 millimeter hole was drilled in the collimator of the opposing detector. The opposed detectors were translated together to scan the patient at each of a number of angles usually 15 degrees apart (see Kuhl and Edwards, "Cylindrical and Section Radioisotope Scanning of Liver and Brain", Radiology, Vol. 83, 926, November, 1964, at page 932) (6). A CRT (cathode ray tube) beam was swept to form a narrow illuminated line corresponding to the orientation and position of the 6.3 millimeter gamma beam through the patient and as the scan proceeded the brightness of the line on the CRT was varied according to the count rate in the detector; a transverse section image was thus built up on a film viewing the CRT. Kuhl found the transverse section transmission scan to be especially useful for an anatomic orientation of a simultaneous transverse section emission scan of the human thorax and mediastinum.
At the June, 1966 meeting of the Society of Nuclear Medicine in Philadelphia, Dr. Kuhl (D. E. Kuhl and R. Q. Edwards, Abstract A-5 "Reorganizing Transverse Section Scan Data as a Rectilinear Matrix Using Digital Processing", Journal of Nuclear Medicine, Vol. 7, P. 332, (June, 1966), (7), described the use of digital processing of his transverse section scan data to produce a rectilinear matrix image superior to the images obtained with the above method of film exposure summation of count rate modulated CRT lines. The scan data from each detector was stored on magnetic tape, comprising a series of scans at 24 different angles 7.5 degrees apart around the patient. One hundred eighty-one thousand operations were performed in 12 minutes on this data to produce a transverse section image matrix of 10,000 elements.
The process is described in more detail in D. E. Kuhl and R. Q. Edwards, "Reorganizing Data from Transverse Section Scans of the Brain Using Digital Processing", Radiology, Vol. 91, p. 975 (November, 1968) (8). The matrix comprised a 100 by 100 array of 2.5 millimeter by 2.5 millimeter elements. For each picture element the counts recorded on the scan line through the element at each of the 24 scan angles were extracted by programmed search from drum storage, summed, divided by 24 and stored on tape, after which they could be called sequentially to produce a CRT raster scan.
R. A. Crowther, D. J. DeRosier, and A. Klug, in "The Reconstruction of a Three Dimensional Structure from Projections and Its Application to Electron Microscopy", Proceedings of the Royal Society of London, 317A, 319 (1970), (9), developed a formal solution of the problem of reconstructing three-dimensional absorption distributions from two-dimensional electron micrograph projections, using Fourier transformation. They considered a series of 5 degree tilts from +45 degrees to -45 degrees and found that at least .pi.D/d views are required to reconstruct a body of diameter D to a resolution of d.p. 332.
M. Goitein, in "Three Dimensional Density Reconstruction from a Series of Two-Dimensional Projections", Nuclear Instruments and Methods 101, 509 (1972), (10), shows that standard matrix inversion techniques for two dimensional reconstructions require too much storage space. He states that a 50K word memory is required for an inversion of a 225.times.225 matrix for a 15.times.15 element object grid and that with use of overflow memory the execution time increases as the sixth power of the number of cells along the edge of the object grid, p. 511. He proposes an iterative relaxation procedure since an "exact solution" is not computationally accessable for a typical object grid such as 100.times.100 elements. This technique involves adjusting the density of any cell to fit all measurements which involve that cell, "fit" being on the basis of least-squares minimization. He used the Cormack (1964) phantom design as a model, simulated it on a computer, "measured" absorption with a scan of 51 transversely separated lines repeated at 40 uniformly spaced angles, introduced 1% random error in the measurements and computed the absorption distribution in a transverse section view on a 30.times.30 grid using 15 iterations. He also computed absorption distributions in transverse section view using the original absorption data recorded by Cormack (1964) as well as data furnished by others from alpha beam and X-ray beam transmission measurements.
D. Kuhl, R. Q. Edwards, A. R. Ricci and M. Reivich, in "Quantitative Section Scanning Using Orthogonal Tangent Correction", Abstract, Journal of Nuclear Medicine Vol. 13, p. 447 (June, 1972), (11), describe an iterative computation method combining the data from a scan at one angle with the data from a scan at 90 degrees to this angle, and repeating this computation process for a multitude of angles. An iterative correction is continued through all angles, requiring 10 minutes with a Varian 16 bit 8K word core computer (Varian Data Machines, Irvine, Calif.).
All of these methods suffer from certain deficiencies. The errors inherent in such prior art techniques are not easily ascertainable. The time to gather the data is slow; in the case of X-ray diagnosis, this increases the time the patient must be strapped in an uncomfortable position and limits the throughput, i.e., total patient handling capacity, of the machine. It also means that for slices of body regions such as the abdominal cavity, the patient's normal breathing produces motion in the phantom during the taking of measurements and consequent blurring of the output picture, which can mask, for example, the presence of tumors. The time required to reduce the data to picture form is lengthy, typically on the order of a quarter of an hour. Spatial resolution of the output picture is often relatively poor.
D. Boyd, J. Coonrod, J. Dehnert, D. Chu, C. Lim, B. MacDonald, and V. Perez-Mendez, "A High Pressure Xenon Proportional Chamber for X-Ray Laminographic Reconstruction Using Fan Beam Geometry," IEEE Transactions on Nuclear Science, Vol. NS-21, No. 1 (Feb. 1974) (12), describe, at P. 185, a reconstruction method for a fan beam source which employs a convolution method of data reconstruction. This use of a fan beam can result in a reduction in data-gathering time, and a more efficient utilization of radiation flux. However, the fan beam rays are first reordered into parallel beam rays, then a known parallel ray convolution method is employed. This step of first reordering the data introduces a delay. An additional problem with this method is that normal optimization of design criteria in most applications requires that the angle between individual rays of the fan beam be less than the angle of arc between pulses of the source. Thus, there is no one-to-one matchup between fan beam rays and parallel beam rays. As a result, approximations must be made during the reordering step, causing a diminution in resolution in the output picture. Even in the case where there is a one-to-one relationship between fan beam rays and parallel beam rays, the distances between the resultant parallel beam rays will be unequal. Therefore, another set of resolution-diminishing approximations must be made. Another problem with reordering is that reordering forces one to fix irrevocably the number of pulses per revolution of the source. This results in a loss of flexibility because, for example, the wider the object being pictured, the smaller the arcuate angle between pulsing required for the same resolution. If one does not reorder, one can design into the machine convenient means whereby the operator may adjust the arcuate angle between pulsing depending upon the object size.
No prior art method combines the use of a fan beam source and the application of a convolution method of data reconstruction with no intervening reordering of the detected projection profiles over each other. No prior art method is capable of providing an exact reconstruction of a two-dimensional picture from a series of one-dimensional projections when the superior fan beam source is employed.